(*^ ::[ Information = "This is a Mathematica Notebook file. It contains ASCII text, and can be transferred by email, ftp, or other text-file transfer utility. It should be read or edited using a copy of Mathematica or MathReader. If you received this as email, use your mail application or copy/paste to save everything from the line containing (*^ down to the line containing ^*) into a plain text file. On some systems you may have to give the file a name ending with ".ma" to allow Mathematica to recognize it as a Notebook. The line below identifies what version of Mathematica created this file, but it can be opened using any other version as well."; FrontEndVersion = "NeXT Mathematica Notebook Front End Version 2.2"; NeXTStandardFontEncoding; fontset = title, inactive, noPageBreakBelow, noPageBreakInGroup, nohscroll, preserveAspect, groupLikeTitle, center, M7, bold, L1, e8, 24, "Times"; ; fontset = subtitle, inactive, noPageBreakBelow, noPageBreakInGroup, nohscroll, preserveAspect, groupLikeTitle, center, M7, bold, L1, e6, 18, "Times"; ; fontset = subsubtitle, inactive, noPageBreakBelow, noPageBreakInGroup, nohscroll, preserveAspect, groupLikeTitle, center, M7, italic, L1, e6, 14, "Times"; ; fontset = section, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, grayBox, M22, bold, L1, a20, 18, "Times"; ; fontset = subsection, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, blackBox, M19, bold, L1, a15, 14, "Times"; ; fontset = subsubsection, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, whiteBox, M18, bold, L1, a12, 12, "Times"; ; fontset = text, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, L1, 12; fontset = smalltext, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, L1, 10, "Times"; ; fontset = input, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeInput, M42, N23, bold, L1, 12, "Courier"; ; fontset = output, output, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, L-5, 12, "Courier"; ; fontset = message, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, L1, 12, "Courier"; ; fontset = print, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, L1, 12, "Courier"; ; fontset = info, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, L1, 12, "Courier"; ; fontset = postscript, PostScript, formatAsPostScript, output, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeGraphics, M7, l34, w282, h287, L1, 12, "Courier"; ; fontset = name, inactive, noPageBreakInGroup, nohscroll, preserveAspect, M7, italic, B65535, L1, 10, "Times"; ; fontset = header, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, italic, L1, 12, "Times"; ; fontset = leftheader, 12; fontset = footer, inactive, nohscroll, noKeepOnOnePage, preserveAspect, center, M7, italic, L1, 12, "Times"; ; fontset = leftfooter, 12; fontset = help, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, L1, 12; fontset = clipboard, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, L1, 12; fontset = completions, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, L1, 12, "Courier"; ; fontset = special1, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, L1, 12; fontset = special2, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, L1, 12; fontset = special3, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, L1, 12; fontset = special4, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, L1, 12; fontset = special5, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, L1, 12; paletteColors = 128; automaticGrouping; currentKernel; ] :[font = title; inactive; preserveAspect; startGroup] Analysis of a Simple Structure :[font = section; inactive; preserveAspect; startGroup] BRIEF ABSTRACT :[font = subsection; inactive; preserveAspect; endGroup] In this multivariate calculus application, we determine the position of a truss joint by minimizing potential energy. Physics preliminaries are provided. :[font = section; inactive; Cclosed; preserveAspect; startGroup] GENERAL INFORMATION :[font = subsection; inactive; preserveAspect] FileName: STRUCT :[font = subsection; inactive; preserveAspect] Full title: Analysis of a Simple Structure :[font = subsection; inactive; preserveAspect] Last Update: 6/5/96 :[font = subsection; inactive; preserveAspect] Developer: Jerry Fine Department of Mechanical Engineering Rose-Hulman Institute of Technology Terre Haute, IN 47803 Phone: 812-877-8353. Email: fine@nextwork.rose-hulman.edu FAX: 812-877-3198 :[font = subsection; inactive; preserveAspect] Contact: Aaron Klebanoff, Department of Mathematics, Rose-Hulman Institute of Technology, Terre Haute IN 47803 USA. Phone: 812-877-8151. Email: Klebanoff@rose-hulman.edu. FAX: 812-877-3198. :[font = subsection; inactive; preserveAspect; endGroup] Support: The production of this material is supported by the National Science Foundation under Division of Undergraduate Education grant DUE-9352849: Development Site for Complex, Technology-Based Problems in Calculus with Applications in Science and Engineering and the Arvin Foundation of Columbus IN. :[font = section; inactive; Cclosed; preserveAspect; startGroup] STATEMENT OF PROBLEM :[font = text; inactive; preserveAspect] A simple structure is shown in the figure below. It consists of 3 bars which share a common pin joint. The bars are also joined to rigid supports using pin joints. In this type of arrangement, called a truss, the bars act as linear springs. They remain straight as a load is applied, stretching and compressing, but not bending. In the problem shown a force load is applied at the common joint. Your task is to find the motion of the joint under that loading. How far does it move horizontally and vertically? Your answer may be given with two numbers: the horizontal and vertical components of the joint's change in position. (Call the former "u" and the latter "v.") :[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; pictureLeft = 0; pictureWidth = 415; pictureHeight = 302] %! %%Creator: Mathematica %%AspectRatio: 0.727711 MathPictureStart /Courier findfont 10 scalefont setfont % Scaling calculations 0 1 0 1 [ [ 0 0 0 0 ] [ 415 302 0 0 ] ] MathScale % Start of Graphics %!PS-Adobe-2.0 EPSF-1.2 %%Creator:Scan %%Title:Pasteboard %%Origin:0 720 %%BoundingBox: 0.0 0.0 415.000 302.000 %%EndComments gsave %%BeginFile:Pasteboard %!PS-Adobe-2.0 EPSF-1.2 %%Creator:Scan %%Title:ConvertedTIFF %%CreationDate:Wed Aug 2 18:02:23 1995 %%Origin:0 720 %%BoundingBox: 0.0 0.0 416.000 302.000 %%EndComments %ImageData: 416 302 2 1 0 104 0 "beginimage" 20 dict begin /rows 302 def /cols 416 def /str1 104 string def /readit {currentfile exch readhexstring pop} def /beginimage {{str1 readit} image} def gsave 1.000 1.000 scale cols rows scale cols rows 2 [cols 0 0 rows neg 0 rows] beginimage FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF3FFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFF3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FF3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF3FFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF CC3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFCFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF3FF0FFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFF0FFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC FFFFF3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFF3FFFFFC3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFFFFC3FFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFFFFFCFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF3F FFFFFFFF0FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFCFFFFFFFFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFFFFFFFF3FFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF3FFFC03FFFFFCFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFF 03FC0FFFFF3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFCFF0FFFFF0FFFF3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFF3F0FFFFFFF0FFF3FFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFF3FFFFFFFCFFFCFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFCFF FFFFFFF3FFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFF3FCFFFF0FFFF3FFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFCFF3FFC0F03FFCFFCFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFF3FFCFFF3FFCFFCFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF3FF3FF 3FFFCFFCFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFCFFCFFF3FFFCFFF3FCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFCFFCFFCFFFFF3FF3FCFFC000000000000000000 00000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF3FFCFFCFFFFF3FF3FCFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFFFFFFFFF3FFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFCFFF 3FFFCFFF3FCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFCFFFF3FF3FFFCFFCFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFF3FFFF3FF0FFF0FFCFFCFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFF3FFC0F03FFCC3CFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFFCFF FF0FFFF3FC3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFFFFFFFFFFAABFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFF3FFFFFCFFFFFFFFF3FFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFCF3FFFFF3FFFFFFFCFFFF0FFFFFFFFFFFFFFFFFFFF FFFFFFFFFF3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFC3FFFF0FFFFFFF0FFFFF0FFF FFFFFFFFFFFFFFFFFFFFFFFFFF3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF3FFCFFFFF0 FFFFF03FFFFFF0FFFFFFFFFFFFFFFFFFFFFFFFFFFF3FFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFCFFFF0FFFFF03FC0FC3FFFFFF0FFFFFFFFFFFFFFFFFFFFFFFFFFF3FFFFF FFFFFFFFC3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFCFFFFF3FFFFFC03FFFCFFFFFFF3FFFFFFFFFFFFFFFF FFFFFFFFFF3FFFFFFFF03F033CFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF3FFFFFC3FFFFFFFFFFF0FFFFFFC 3FFFFFFFFFFFFFFFFFFFFFFFFF3FFFFFFFCFCC303CFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF F03FFFFFFFFF0FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFFFFCFFF FFFFFFFFF0FFFFFFC3FFFFFFFFFFFFFFFFFFFFFFFF3FFFFFFFFFCCFC3CFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFCFFFFFFFFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFCFFFFFFFF0FFFFFFFFF0FF0FFFFFFC3FFFFFFFFFFFFFFFFFFFFFFF3FFFFF FFFF3CFCC3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFFFFFFFCFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFF3FFFFFFFFF0FFFFFFF0FFFF0FFFFFFC3FFFFFFFFFFFF FFFFFFFFFCFFFFFFFFF03CFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFC3FC3FC0FFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFFFFFFFF000FFFCFFFFFF3FFF FFFCFFFFFFFFFFFFFFFFFFFFFCFFFFFFC0FFCCFCFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FCFFF3CF3CF3CFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFFFFFFFFF FF0003FFFFFFC3FFFFFF0FFFFFFFFFFFFFFFFFFFFCFFFFFFFFFFCCFCFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFAABFFCFFF3CFC0F3CFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFF3FFFFFFFFFFFFFFFFFFFFFFFFFC3FFFFFF0FFFFFFFFFFFFFFFFFFFCFFFFFF FFCFCC30FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFAABFFCFFF3CF3CF3CFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFC3FFFFFF0FFFFFFFFF FFFFFFFFF3FFFFFFFFF03F03FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC0ABFFCFCF3CF3CF3CFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFC 3FFFFFF0FFFFFFFFFFFFFFFFF3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC00ABF F000FC3FC33C33FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF3FFFFFFFFFFFFF FFFFFFFFFFFFFFFFCFFFFFFF3FFFFFFFFFFFFFFFF3FFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFF0002ABFFFFFFFFFFFFFFFFFFFFFFFFFF3FFFFFFFFFFFFFFFFFFFFFF FCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF0FFFFFFC3FFFFFFFFFFFFFFCFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFF0000FFFFFFFFFFFFFFFFFFFFFFFFFFFFF3FFFFFF FFFFFFFFFFFFFFFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF0FFFFFFC3FFFFF FFFFFFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00000FFFFFFFFFFFFFFFFFFFF FFFFFFFFF3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFF0FFFFFFC3FFFFFFFFFFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC000003FFFF F0003FFFFFFFCFF00F03F03FC30FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFF0FFFFFFC3FFFFFFFFFFF3FFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFC000000FFFFFFCFF3FFFFFFF0FF3FC30C30FF3CFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF3FFFFFFCFFFFFFFFFFF3FFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFC0000000FFFFFFCFFFFFFFFFCCFF3FCFCCFCFF3CFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC3FFFFFF0FF FFFFFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC0000003FFFFFFCFCFFFFFFFFCFF0 3CFCCFCFF3C0FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFC3FFFFFF0FFFFFFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC000000FFFFFF FC00FFF003FFCFFF0CFCCFCFF3CF3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFC3FFFFFF0FFFFFFFCFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFF000003FFFFFFFCFCFFFFFFFFCFFFCCFCCFCFF3CF3FFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFFFF0FFFFFF3FFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFF000003FFFFFFFCFFFFF003FFCFFFCCFCCFCFF3CF3FFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF0FFFFFF F3FFFFF3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC00000FFFFFFFFCFFFFFFFFFFCFCF 0C30C30FF3CF3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFF0FFFFFFC3FFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000003FFFFFFF F00FFFFFFFFF03F03F03F03FC0C0FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFF0FFFFFFC3FFCFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FF003C003FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF3FFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF0FFFFFFC3FCFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFC00FF00FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF3FFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF3FF FFFFC3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF003FFC3FFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFF3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFC3FFFFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000FFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC3FFFFFF0FFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC 00FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC3FFFFFF0FFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFF003FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF C3FFFFFF0FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC00FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFCFFFFFFF0FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC00FFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF0FFFFFFF3FFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF003 FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF0FFFFFFC3FFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFC00FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFF0FFFFFFC3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFC003FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC0FFFFFFFFFFFFF0FF FFFFCFF03F03FF3FFFFFF0FFFFFFC3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF003FFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF3 FFFFFFFFFFFFFCFFFFFF0FC30C30FFFFFFFFFF3FFFFFFC3FFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC00FFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFF3FFFFFFFFFFFCFCFFFFFCCFCFCCFCFFFFFFFFFFC3FFFFFFCF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFF003FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF3FFF0F30FF0000C0FCFFFCFCFCCFCFC33 0FFFFFFC3FFFFFF0FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFF003FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF3FFCF3CF3CF3CFCF3 FFFFCFCFCCFCFF3CF3FFFFFFC3FFFFFF0FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC00FFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF3 FFC03CF3CF3CFCF3FFFFCFCFCCFCFF3CF3FFFFFFFC3FFFFFF0FFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF003FFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFF3FFCFFCF3C0FCFCF3FFFFCFCFCCFCFF3CF3FFFFFFFFCFFFFF FF0FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFF000FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF3F3C3CCF3F3FCFCF3FFFFCFC30C30FF3C F3FFFFFFFFF0FFFFFFF0FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFC00FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC003F03030F03F0030 CFFF03F03F03FC0030FFFFFFFFFF0FFFFFFF3FFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF003FFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFCFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF0FFFFFFC3FFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC00FFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFCFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF0F FFFFFC3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFC00FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF03FFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFF3FFFFFFC3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFF003FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC3FFFFFFC3FFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC00FFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC3FFFFFFCFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF003FFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FC3FFFFFF0FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FF003FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFC3FFFFFF0FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFC00FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFFFF0FFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF003FFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF0FFFFFFF0FFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000FFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFF0FFFFFFF3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC 00FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFF0FFFFFFC3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFF003FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFC30FFFFFFFFFFFFFF0F FFFFFCFF00F03FFC0FC0FC0FC30FFF33FFFFFFF0FFFFFFC3FFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC00FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF3CF FFFFFFFFFFFFFFCFFFFFF0FF3FC30FF0C30C30C3F3CFFF3FFFFFFFFF3FFFFFFC 3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC00FFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFCFFF3CFFFFFFFFFFFFFFFCFFFFFCCFF3FCFCFF3F33F33F3F3CFFF3F FFFFFFFFC3FFFFFFC3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF003 FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFF03000C000C3FC3FC0FC0FFFCF3CFFFCFF03CFCFF3 F33F33F3F3C0FCC330FFFFFFFC3FFFFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFC00FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCF3CFCF3CF3CF3CF3CF3CFFFCC FFFFFCFFF0CFCFF3F33F33F3F3CF3CF3CF3FFFFFFFC3FFFFFF0FFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFC003FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC3FCFCF3CF 3CF00F0FF0FFFFC3FFFFFCFFFCCFCFF3F33F33F3F3CF3CF3CF3FFFFFFFFC3FFF FFF0FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF003FFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFC3CFCF3CF3CF3FFF0FF0FFFCCFFFFFCFFFCCFCFF3F33F33F3F3CF33F3 CF3FFFFFFFFFCFFFFFFF0FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC00FFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFCF3CFCF3CF3CF0F33CF3CFFFCF3FFFFCFCF0C30FF0 C30C30C3F3CF33F3CF3FFFFFFFFFF0FFFFFFF0FFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFF003FFFFFFFFFAABFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC0FF0033CC0C3C0F03F03F3FCF 0CFFF03F03F03CFC0FC0FC0FC0C0F3C0030FFFFFFFFFFF0FFFFFFF3FFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFF003FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFF3FFFFFFFFFFFFFFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF0 FFFFFFC3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC00FFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFFFFFFFFFFFFFF3FFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFF3FFFFFFC3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF003FFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC3FFFFFFC3FFFFFFFFFFFFFFFFFFFFFF FFFFFFFC00FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC3FFFFFFC3FFFFF FFFFFFFFFFFFFFFFFFFFFFC00CFFFFFFFFFFFFC3FFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFC3FFFFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFF003F3FFFFFF03F033CFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFC3FFFFFF0FFFFFFFFFFFFFFFFFFFFFFFFFC00FF3FFFFF CFCC303CFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFFFF0FFFFFFFFFFFFFFFFFFF FFFFC003FFCFFFFFFFCCFC3CFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF0FFFFFFF0FF FFFFFFFFFFFFFFFFFFFF003FFFCFFFFFFF3CFCC3FFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFF0FFFFFFF0FFFFFFFFFFFFFFFFFFFFC00FFFFF3FFFFF03CFCFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFF0FFFFFFF3FFFFFFFFFFFFFFFFFFF003FFFFF3FFFF FFCCFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF0FFFFFFC3FFFFFFFFFFFFFFF FF003FFFFFFCFFFFFFCCFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF3FFFFFF C3FFFFFFFFFFFFFFFC00FFFFFFFCFFFFCFCC30FFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFC3FFFFFFC3FFFFFFFFFFFFFF003FFFFFFFF3FFFF03F03FFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFC3FFFFFFC3FFFFFFFFFFFF000FFFFFFFFF3FFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC3FFFFFFCFFFFF00FFFFC 00FFFFFFFFFF3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC3FF FFFF0FFC0FF03FF003FFFFFFFFFF3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFCFFFFFFF0C3FFFFC3C00FFFFFFFFFFF3FFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFF0FFFFFFC3FFFFFFC00FFFFFFFFFFFF3FFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF0FFFFFCFFFFFFF003 FFFFFFFFFFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF 0FFFF3FFFFFFC00FFFFFFFFFFFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFF0FFF3FFFC3C000FFFFFFFFFFFFFCFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF3FCFFF03C003F3FFFFFFFFFFFFCFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC3CFFF3FC00FF3 FFFFFFFFFFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFC0FFCFF003FF3FFFFFFFFFFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFF0FFCF0033FFCFFFFFFFFFFFFCFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF3FF3C00FCFFCFFFFFFFFFFFFF3FF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF3FF3C03FCFF0 00000000000000000000000000000000000000000000000000000FFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFF3FFCF0FF3FFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFCFFCFFFF3FF3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFC3FFC3FF0FFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFF03C0FFF0 FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFF3FFFC3FFFCF3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFF3FFFFFFFFCF3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCCFFFFFFFF3FCFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF3C3FFFFFFC3F F3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFCFFC3FFFFC3FFF3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFCFFFC0FF033FFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF3FFFF300FFCFFFCFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFCFFFFFCFF FF3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FF3FFFF3FFFFFF3FFF3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFCFFFFF3FFFFFFCFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF3FFFFCFFFFFFFCFFFCFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFF3FFFFFFFF3 FFF3FFFFFFFFFFFFFFCFC30FFFFFFFFFFFFFF0FFFFFF03F03F03FFC0FC0FC0FC 30FFF33FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF CFFFFCFFFFFFFFF3FFF3FFFFFFFFFFFFFFFF3CFFFFFFFFFFFFFFFCFFFFFCFCC3 0C30FF0C30C30C3F3CFFF3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFF3FFFF3FFFFFFFFFCFFFCFFFFFFFFFFFFCFFF3CFFFFFFFFFF FFFFFCFFFFFFFCCFCCFCFF3F33F33F3F3CFFF3FFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFCFFFFFFFFFFCFFFF3FFFFFFFFF03 000C000C3FC3FC0FC0FFFCF3CFFFFCCFCCFCFF3F33F33F3F3C0FCC330FFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF3FFFF3FFFFFFFFFFF 3FFF3FFFFFFFFCF3CFCF3CF3CF3CF3CF3CFFFCCFFFFFF3CFCCFCFF3F33F33F3F 3CF3CF3CF3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCF FFFF3FFFFFFFFFFF3FFFCFFFFFFFFC3FCFCF3CF3CF00F0FF0FFFFC3FFFFFCFCF CCFCFF3F33F33F3F3CF3CF3CF3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFF3FFFFCFFFFFFFFFFFFCFFFCFFFFFFFFFC3CFCF3CF3CF3FFF0F F0FFFCCFFFFF3FCFCCFCFF3F33F33F3F3CF33F3CF3FFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFF3FFFFFFFFFFFFCFFFF3FFFFFFFCF3 CFCF3CF3CF0F33CF3CFFFCF3FFFCFCC30C30FF0C30C30C3F3CF33F3CF3FFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFCFFFFFFFFFFFFF F3FFF3FFFFFFFC0FF0033CC0C3C0F03F03F3FCF0CFFC00F03F03CFC0FC0FC0FC 0C0F3C0030FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF3FF FF3FFFFFFFFFFFFFFCFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFF3FFFFFFFFFFFF FFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFCFFFFCFFFFFFFFFFFFFFFCFFFCFFFFFFFFFFFFFFFFFFFFFFFFFF FFCFFFFFFFFFFFFFFFFF3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFF3FFFF3FFFFFFFFFFFFFFFF3FFF3FFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFF3FFFFFFFFFFFFFF FF3FFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF3FFFF CFFFFFFFFFFFFFFFFFCFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFF3FFFF3FFFFFFFFFFFFFFFFFCFFFF3FFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF03FFFFFFFFFFFF C3FFFFF003C03FCFFFFFFFFFFFCFFFFCFFFFFFFFFFFFFFFFFFF3FFF3FFFFFF03 FFFFFFFFFFFFC3FFFFF003C03FCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFCFFFFFFFFFFFFFF3FFFFF3F3CFFFFFFFFFFFFFFF3FFFF3FFFFFFFFFFFFFFFF FFF3FFFCFFFFFFCFFFFFFFFFFFFFF3FFFFF3F3CFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFCFFFFFFFFFFFF3F3FFFFFFCFCFFFFFFFFFFFFFFCFFFFCF FFFFFFFFFFFFFFFFFFFCFFFCFFFFFFCFFFFFFFFFFFF3F3FFFFFFCFCFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFC3CC3FC000303F3FFFCFC0FF0C C3FFFFFFF3FFFFCFFFFFFFFFFFFFFFFFFFFF3FFF3FFFFFCFFFC3CC3FC000303F 3FFFCFC0FF0CC3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFF3CF3CF3CF3 F3CFFFFF3FFC3FCF3CFFFFFFCFFFFF3FFFFFFFFFFFFFFFFFFFFF3FFF3FFFFFCF FF3CF3CF3CF3F3CFFFFF3FFC3FCF3CFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFCFFF00F3CF3CF3F3CFFFFF3FFF3FCF3CFFFFFF3FFFFCFFFFFFFFFFFFFFFFFF FFFFCFFFCFFFFFCFFF00F3CF3CF3F3CFFFFF3FFF3FCF3CFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFCFFF3FF3CF03F3F3CFFFFCFFFF3FCF3CFFFFFF3FFFF3FF FFFFFFFFFFFFFFFFFFFFCFFFF3FFFFCFFF3FF3CF03F3F3CFFFFCFFFF3FCF3CFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFCF0F33CFCFF3F3CFFFFCFF3C3FCF 3CFFFFFCFFFFCFFFFFFFFFFFFFFFFFFFFFFFF3FFF3FFFFCFCF0F33CFCFF3F3CF FFFCFF3C3FCF3CFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000FC0C0C3C0FC 00C33FFCFFC0FF000C3FFFF3FFFF3FFFFFFFFFFFFFFFFFFFFFFFF3FFFCFFFF00 0FC0C0C3C0FC00C33FFCFFC0FF000C3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFF3F3FFFFFFFFFFFFFFFFFFFFFFFCFFFFCFFFFFFFFFFFFFFFFFFFF FFFFFCFFFCFFFFFFFFFFFFFF3F3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFF3F3FFFFFFFFFFFFFFFFFFFFFFF3FFFFCFFFF FFFFFFFFFFFFFFFFFFFFFCFFFF3FFFFFFFFFFFFF3F3FFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC0FFFFFFFFFFFFFFFFFF FFFFFCFFFFF3FFFFFFFFFFFFFFFFFFFFFFFFFF3FFF3FFFFFFFFFFFFFC0FFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFF3FFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFCFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF3FFFF3FFFFFFFFFFFFFFFFFFFFF FFFFFFCFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFCFFFFFF FFFFFFFFFFFFFFFFFFFFFFF3FFF3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFF3FFFF3FFFFFFFFFFFFFFFFFFFFFFFFFFFFF3FFF3FFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFCFFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFCFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF3FFFFCFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFCFFFF3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFF3FFFFFFF FFFFFFFFFFFFFFFFFFFFFFFF3FFF3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFCFFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF3FFFCFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFF3FFFF3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFCFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFCFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFCFFFF3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF3FFFF3FFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFF3FFF3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFC3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCF C30FFFFFFFFFFFFFF0FFFFFF03F03F03FFC0FC0FC0FC30FFF33FFFFFFFFFFFFF CFFFFF3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFCFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFCFF03F003CFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFF3CFFFFFFFFFFFFFFFCFFFFFCFCC30C30FF0C30C30C3F3CFF F3FFFFFFFFFFFFFF3FFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFCFF FFFFC0000000003FFFFFFFFFFFFFFFFFF0FCFCF3F3CFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFF3CFFFFFFFFFFFFFFFCFFFFFFFCCFCCFC FF3F33F33F3F3CFFF3FFFFFFFFFFFFFCFFFFF3FFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFF3FFF3FFFC03FFFFFFFFFC03FFFFFFFFFFFFFFFCCFFFCF3F3CFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF03000C000C3FC3FC0FC0FF FCF3CFFFFCCFCCFCFF3F33F33F3F3C0FCC330FFFFFFFFFFCFFFFCFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFF3FFFCFC03FFFFFFFFFFFFFC03FFFFFFFFFFFFF FCFFFCF03C3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCF3CFCF 3CF3CF3CF3CF3CFFFCCFFFFFF3CFCCFCFF3F33F33F3F3CF3CF3CF3FFFFFFFFF3 FFFF3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFCC3FFFFFFFFFFFFFFF FFC0FFFFFFFFFFFFFCFFF3FF0FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFC3FCFCF3CF3CF00F0FF0FFFFC3FFFFFCFCFCCFCFF3F33F33F3F3CF3 CF3CF3FFFFFFFFCFFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFF3 FFFFFFFFFFFFFFFFFFFF03FFFFFFFFFFFCFFCFFFCFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFC3CFCF3CF3CF3FFF0FF0FFFCCFFFFF3FCFCCFC FF3F33F33F3F3CF33F3CF3FFFFFFFF3FFFF3FFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFF3FFF3FFFFFFFFFFFFFFFFFFFFFCFFFFFFFFFFFCFF3FFFCFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCF3CFCF3CF3CF0F33CF3CFF FCF3FFFCFCC30C30FF0C30C30C3F3CF33F3CF3FFFFFFFCFFFFF3FFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFF3FFFCFFFFFFFFFFFFFFFFFFFFFF0FFFFFFFFF FCFCFCCF0FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC0FF003 3CC0C3C0F03F03F3FCF0CFFC00F03F03CFC0FC0FC0FC0C0F3C0030FFFFFFF3FF FFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFCFFFFFFFFFFFFFFFF FFFFFFF0FFFFFFFFF03C00F03FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF3FFFFFFFFFFFFFFFFCFFFFFFFFFFFFFFF FFFFFFFFFFFFF3FFFF3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF3FFF 3FFFFFFFFFFFFFFFFFFFFFFF0FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFFFFFFFFFFFFFF 3FFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFF3FFF3FFFFFFFFFFFFFFFFFFFFFFFF0FFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF3FFFF3FFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFCFFFFFFFFFFFFFFFFFFFFFFFFC3FFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFF CFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFCFFFFFFFFFFFFFFF FFFFFFFFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFF3FFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF3FF F3FFFFFFFFFFFFFFFFFFFFFFFFF0FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFF3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFF3FFFCFFFFFFFFFFFFFFFFFFFFFFFFFF3FFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF3FFFFCFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFCFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF3FFFF3 3FFFFFFFFFFFFFFEAAFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFF3FFFFFFFFFFFFF FFFFFFFFFFFFF3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFCFFFFCFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF3F FF3FFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFF3FFFF3FF3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFF3FFFCFFFFFFFFFFFFFFFFFFFFFFFFFFF3FFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFCFFFCFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFCF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF3FFFFCFF FF3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF3FFF3FFFFFFFFFFFF FFFFFFFFFFFFFFF3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFCFFFFF3FFFFCFFFFFFFFFFFFF0FFFFFFFFFFFFFFFFFFFFFFFFFFFFFF3 FFF3FFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFF3FFFFCFFFFFF3FFFFFFC03C00F3FFFFFFFFFFFFFF FFFFFFFFFFFFFFFCFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFF3FFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF3FFFF3FFFFFFCFFFFFFCFFCFC F3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFF3FFFFFFFFFFFFFFFFFFFFFFFFFFF CFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFCFFFF FFFF3FFFFFCFFCFCF3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFF3FFF3FFFFFFFFFFF FFFFFFFFFFFFFFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFF3FFFF3FFFFFFFFCFFFFFC0FC0F0FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF 3FFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFF3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFCFFFFCFFFFFFFFFF3FFFFFC3FC3FFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFCFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF3FFFFCFFFFFFFFFFCFFFFFF3FF3 FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFF3FFFFFFFFFFFFFFFFFFFFFFFFFF FCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFF3FFFFF FFFFFCFFFFFF3FF3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF3FFF3FFFFFFFFFF FFFFFFFFFFFFFFFFFF3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFCFFFFCFFFFFFFFFFFF3FFF3C33C3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FCFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFF3FFFF3FFFFFFFFFFFF3FFFC0FC0FFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFCFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFCFFFFFFFFFFFFFCFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF3FFF3FFFFFFFFFFFFFFFFFFFFFFFFF FFF3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF3FFFF3FFFFFFF FFFFFFF3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF3FFFCFFFFFFFFF FFFFFFFFFFFFFFFFFFF3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFCFFFFF3FFFFFFFFFFFFFF3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFCFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFF3FFFFCFFFFFFFFFFFFFFFCFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFCFFFF3FFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFF3FFFFFFFFFFFFFFFF3FFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF3FFF3FFFFFFFFFFFFFFFFFFFFFFFF FFFF3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFCFFFFFFFFF FFFFFFFF3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF3FFFCFFFFFFFF FFFFFFFFFFFFFFFFFFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF F3FFFF3FFFFFFFFFFFFFFFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFCFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFCFFFFCFFFFFFFFFFFFFFFFFFCFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFF3FFF3FFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFC000FFF3FFFF3FFFFFFFFFFFFFFFFFFCFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF3FFF3FFFFFFFFFFFFFFFFFFFFFFF FFFFF3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC3FFF00CFFFFF3FFFFFFFFFF FFFFFFFFF3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFCFFFFFFF FFFFFFFFFFFFFFFFFFFFF3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF03FFFFFF3 FFFFCFFFFFFFFFFFFFFFFFFFF3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFCFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFF3FFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFF3FFFFFFCFFFFF3FFFFFFFFFFFFFFFFFFFF3FFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFF3FFF0000003FFFFFFFFFFFFFFFFFFFFFCFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFF0FFFFFFFCFFFFCFFFFFFFFFFFFFFFFFFFFFCFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF3FFFCFFFFFC0FFFFFFFFFFFFFFF FFFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFFFFF3FFFF3FFFFFFFFFFFF FFFFFFFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFCFFFFFF F0FFFFFFFFFFFFFFFFFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF3FFFFFFFCFF FFCFFFFFFFFFFFFFFFFFFFFFFF3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFCFFFF3FFFFFFF0FFFFFFFFFFFFFFFFFFCFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFCFFFFFF00FFFFF3FFFFFFFFFFFFFFFFFFFFFFF3FFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFF33FFF3FFFFFFFF3FFFFFFFFFFFFFFFFFF3FFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFF3FFFFC0FF03FFF3F3FFFFFFFFFFFFFFFFFFFFF3FFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCF3FFFC00FFFFFFCFFFFFFFFFFFF FFFFFF3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF3FFFC3FFFFC3FCFF3FFFFFFFFFFF FFFFFFFFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFCFFC0FF03F FFFF3FFFFFFFFFFFFFFFFF3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFC3FFFFFFC 33FFCFFFFFFFFFFFFFFFFFFFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFF3FF3C3FFFFC3FFFFCFFFFFFFFFFFFFFFFF3FFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFF3FFFCFFFFFFFF3FFFF3FFFFFFFFFFFFFFFFFFFFCFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFCFFF03FFFFFFC3FFFF3FFFFFFFFFFFFFFFFCFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFCFFFF3FFFFFFFFCFFFF0FFFFFFFFFFFFFFFFFFFFCFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFCFFFFFFFF3FFFFCFFFFFFFFFF FFFFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF3FFFF3FFFC3FFFCFFFFCFFFFFFFFFF FFFFFFFFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFF0FFFFFFFF CFFFFF3FFFFFFFFFFFFFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF3FFFCFFF03C0FF F3FFFCFFFFFFFFFFFFFFFFFFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFF3FFF33FFC3FFFCFFFFF3FFFFFFFFFFFFFFFCFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FCFFFFCFFF3FFCFFF3FFFCFFFFFFFFFFFFFFFFFFFFF3FFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFF3FFCFFF03C0FFF3FFFFCFFFFFFFFFFFFFFFCFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFF3FFFFCFFCFFFF3FF3FFFCFFFFFFFFFFFFFFFFFFFFF3FFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF3FFCFFF3FFCFFF3FFFFCFFFFFFFFF FFFFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFCFFFFF3FFCFFFF3FFCFFFF3FFFFFFFFF FFFFFFFFFFF3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF3FFCFFCFFFF3F F3FFFFF3FFFFFFFFFFFFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF0FFF3FFFFF3FF3FFFFCF FCFFFF3FFFFFFFFFFFFFFFFFFFF3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFF3FF3FFCFFFF3FFCFFFFFCFFFFFFFFFFFFFFCFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF3FC FFFFFF3FF3FFFFCFFCFFFCFFFFFFFFFFFFFFFFFFFFF3FFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFF3FF3FF3FFFFCFFCFFFFFCFFFFFFFFFFFFFFCFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFCFCFFFFFF3FFCFFFF3FFCFFFCFFFFFFFFFFFFFFFFFFFFF3FFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF3FF3FF3FFFFCFFCFFFFFF3FFFFFFF FFFFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFF33FFFFFFCFFCFFFF3FF3FFFCFFFFFFFFFF FFFFFFFFFFF3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF3FF3FFCFFFF3F FCFFFFFF00000000000000000000000000000000000000000000000000000FFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC3FFFFFFCFFC3FFC3F F3FFFCFFFFFFFFFFFFFFFFFFFFF3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFF3FFCFFCFFFF3FF3FFFFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC FFFFFFCFFF03C0FFF3FFF00000000000000000000000000000000000003FFFFF FFFFFFFFFFFFFFFFFFF3FFCFFC3FFC3FF3FFFFFFCFF0FFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFF3FFFFFF3FFFC3FFFCFFFF3FFFFFFFFFFFFFFFFFFFFFCFFFF FFFFFFFFFFCFFFFFFFFFFFFFFFFFFFFFFFF3FFCFFF03C0FFF3FFFFFFF30FFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC3FFFFF3FFFFFFFFCFFFF3FFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF3FFF3FFFC3FFF CFFFFFFFF0FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFFCFFFFFFFF 3FFFF3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFF3FFF3FFFFFFFFCFFFFFFF0FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FF3FFFFC3FFFFFFC3FFFF3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFCFFFCFFFFFFFF3FFFFFF0FFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFCFFFFFC3FFFFC3FFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFC3FFFFFFC3FFFFF0FFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF0FFFFFC0FF03FFFFFCFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF3FFFC3FFFFC3 FFFFF0FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF3FFFFFF00FFF FFFF3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFF3FFFFC0FF03FFFFF0FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFCFFFFFFFFFFFFFFF3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFCFFFFFF00FFFFFF0FFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFF0FFFFFFFFFFFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFFFFFFFFFF0FFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF3FFFFFFFFFFFF3FFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF3FFFFFFFFFF F0FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFFFFFF FFF3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFF3FFFFFFFFFF0FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFF3FFFFFFFFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFCFFFFFFFFF0FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFC3FFFFFFFFF3FFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFFFFC0FFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFFFFFF3FFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF3FFFFFC3FF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF3FFFFFF FCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFCFFFFC3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFC3FFFFFF3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFF3FFC3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF3FC3FFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF3FFFC3FFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCC3FFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFF3 FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFC3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFF0FCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFC3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFF33FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC3FFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC3FFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF0F FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFC3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFF3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFC3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC3FFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF3FFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC3FFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF C3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF3FFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF grestore end %%EndFile grestore %End of Graphics MathPictureEnd :[font = subsection; inactive; preserveAspect; startGroup] Useful background information: read this to learn about spring behavior. :[font = text; inactive; preserveAspect; endGroup] A linear spring is a mechanical device which transmits a force, F, that is directly proportional to the stretch, or length change, d, (from its standing equilibrium) that it experiences. We write F = k d, where the constant of proportionality, k, is called the spring stiffness. The units of stiffness are force per length. The length change, d, is calculated as the difference between final length, Lf and initial, unloaded length Li. d = Lf - Li. The truss bars in this problem act as though they were springs. Their stiffnesses and initial lengths are given in the figure. As a linear spring changes length, it stores elastic potential energy, U, a quadratic function of d. In fact, U = 1/2 k d2. Note that the same energy will be stored if the spring stretches one inch or compresses one inch. ;[s] 11:0,0;470,1;471,2;503,3;504,4;577,5;578,6;582,7;583,8;903,9;904,10;1004,-1; 11:1,11,8,Times,0,12,0,0,0;1,11,8,Times,64,12,0,0,0;1,11,8,Times,0,12,0,0,0;1,11,8,Times,64,12,0,0,0;1,11,8,Times,0,12,0,0,0;1,11,8,Times,64,12,0,0,0;1,11,8,Times,0,12,0,0,0;1,11,8,Times,64,12,0,0,0;1,11,8,Times,0,12,0,0,0;1,11,8,Times,32,12,0,0,0;1,11,8,Times,0,12,0,0,0; :[font = subsection; inactive; preserveAspect; startGroup] Useful background information: read to learn what static "equilibrium" means. :[font = text; inactive; preserveAspect; endGroup; endGroup] The structure is assumed to be able to resist the load without failing in any way. The common joint will move (we hope only slightly) and the members will share the load, transmitting it to the grounded supports. There will then be no further motion of any kind. This situation is called static equilibrium. Solving this problem means coming up with a mathematical description of static equilibrium. There are two alternatives. The first has to do with forces. One might write down equations which state that the sum of the forces acting on each bar is zero. A good approach is to just consider the equilibrium of the common joint. The forces acting on the joint must have a zero vector sum. Therefore, the forces in the bars and the load must also sum to zero. The second approach has to do with energy. As the joint moves, each of the bars strains and stores elastic potential energy. At the same time the load also moves, reducing the potential energy of the whole structure. Equilibrium is reached when the total potential energy (elastic minus potential energy of loads) is at a minimum. THE KEY TO THE PROBLEM IS TO MINIMIZE THE POTENTIAL ENERGY OF THE STRUCTURE. This is a problem in the calculus of several variables. :[font = section; inactive; Cclosed; preserveAspect; startGroup] KEYWORDS :[font = text; inactive; preserveAspect; endGroup] Structural analysis, elastic potential energy, static equilibrium, minimization of function :[font = section; inactive; Cclosed; preserveAspect; startGroup] TEACHER NOTES :[font = subsection; inactive; Cclosed; preserveAspect; startGroup] ISSUES RELATED TO THE PROBLEM :[font = text; inactive; preserveAspect; endGroup] This is not commonly known outside of the world of structural engineering, but describing the static equilibrium of structures mathematically amounts to looking for stationary points for a function of multiple variables. These variables are often the displacements (position changes) of key points in the structure. Therefore, the structures problem is strongly linked to multi-variate calculus. This problem is intended to motivate the study of multivariate calculus by providing a "real world" example. The difficulty with the example lies in its complexity. Even for a two-variable problem, the function to be minimized is complex both to write down and to deal with. It would be hoped that the student has access to technology which would allow the student to deal effectively with this complexity. An important issue with almost any structure is "linearity." If the structure behaves linearly: (1) the members have linear force displacement relationships, F = k d; AND (2) the "stretch" or length change is a linear function of u and v, the displacement components. In the first solution given below, the structure is only linear in the first of these two senses. However, it makes very great sense to linearize the "stretch" displacement relationship for most structures, because the displacements are so small compared to the lengths of the bars. This is an approach that might be considered to help the analysis if there is not a CAS available. It is illustrated below. The energy functional becomes quadratic, and the equilibrium equation, obtained through partial differentiation, are linear. This approach is illustrated in the solution section. :[font = subsection; inactive; Cclosed; preserveAspect; startGroup] Prerequisites :[font = text; inactive; preserveAspect; endGroup] The student may never have thought about structural analysis. He or she might not be very interested in it from an engineering point of view, but the problem does relate the minimization of a function of two variables to an important class of problems in technology. The student needs to have some familiarity with simple geometry -- such as the distance formula -- in order to find the new lengths and hence the stretches, in terms of the displacement components, and the data. The student needs to know how to calculate the work done by a constant force acting in a two dimensional plane. This is needed to find the potential energy contribution of the load -- it is just the work of this force with the sign changed. If the external load force (gravity for example) does positive work on the structure, then the potential energy decreases, and visa-versa. The student needs to know about energy storage in springs. This is included in the explanation of the problem statement given above. The student needs to be comfortable with the mathematical description of static equilibrium as the minimal potential energy state of the structure. The student needs to know how to minimize a function of several variables. :[font = subsection; inactive; Cclosed; preserveAspect; startGroup] Time allotment - time management :[font = text; inactive; preserveAspect; endGroup] This problem really needs the technological boost of a computer algebra system. It would be possible to work it by hand if the student were: (1) very patient and accurate (2) was good at shortcuts -- which in this case amounts to a linearization of the elastic strain energy function. Still, it would take 2 or 3 hours to produce a carefully worked solution. With the use of a computer algebra system, and assuming that the student understands what he or she is about, the problem could be completed and explored in about an hour. The background material might take 15 minutes to assimilate. :[font = subsection; inactive; Cclosed; preserveAspect; startGroup] Expectations :[font = text; inactive; preserveAspect; endGroup] Some students, perhaps those with some physics or beginning statics under their belt, may try to write down force equilibrium equations for the common joint. This is a very messy way to approach the problem, as they will find out. Hopefully, they will follow the hint and take the energy point of view. An early source of trouble might be writing the "d" for the spring based on the displacement components, and the data. A very common problem would be to get the sign of the load term wrong. Students who are adept at using the CAS will like this problem. :[font = subsection; inactive; Cclosed; preserveAspect; startGroup] Future payoffs :[font = text; inactive; preserveAspect; endGroup] This problem makes an excellent introduction to a more advanced study of structures. It also has relevance to explanations of the finite element method. :[font = subsection; inactive; Cclosed; preserveAspect; startGroup] Extensions :[font = text; inactive; preserveAspect; endGroup] Instead of having two degrees of freedom, one could have as many as 8. After all, there are 4 joints in the problem with a u and a v at each one. (The symbol u stands for horizontal displacement and v stands for vertical displacement.) So one could write the total potential energy in terms of these eight unknowns. The problem is that there are obvious constrains on 6 of the variables. These could be imposed with Lagrange multipliers, and the problem could be solved with the same answer as above. But, there would now be more information. The Lagrange multipliers have a physical interpretation: they are the reactions at the supports. In other words, the Lagrange multipliers are the x and y force components at the fixed joints which hold the structure in static equilibrium. Clearly, structures with much greater complexity could be considered if one had a CAS. :[font = subsection; inactive; Cclosed; preserveAspect; startGroup] References and Sources :[font = text; inactive; preserveAspect; endGroup; endGroup] A First Course in the Finite Element Method by Daryl L. Logan. PWS Kent, 1986, ISBN 0-534-05394-7. See Chapter 3. :[font = section; inactive; Cclosed; preserveAspect; startGroup] POSSIBLE SOLUTION(S) :[font = subsection; inactive; preserveAspect; startGroup] Input the Data :[font = text; inactive; preserveAspect] ki = stiffness coefficient in lb/in of bar i Li = length of bar i fi = angle from the horizontal of bar i. F = external load fF = orientation angle of external load with respect to + x direction. ;[s] 1:0,0;203,-1; 1:1,13,10,Times,0,14,0,0,0; :[font = input; preserveAspect; endGroup] data = { k1 -> 150000, L1 -> 100, f1 -> -30 Degree, k2 -> 200000, L2 -> 75, f2 -> 55 Degree, k3 -> 200000, L3 -> 75, f3 -> 125 Degree, F -> 1500, fF -> 30 Degree }//N; :[font = subsection; inactive; Cclosed; preserveAspect; startGroup] Set up the elastic potential energy contributions of each bar :[font = subsubsection; inactive; preserveAspect; startGroup] Bar length changes :[font = text; inactive; preserveAspect] u -- horizontal displacement of common joint v -- vertical displacement of common joint. d1, d2, d3 --- net length changes in bars 1, 2, and 3 respectively. :[font = input; preserveAspect; endGroup] d1 = Sqrt[ (L1 Cos[f1]+u)^2 + (L1 Sin[f1]+v)^2 ] - L1 /. data; d2 = Sqrt[ (L2 Cos[f2]+u)^2 + (L2 Sin[f2]+v)^2 ] - L2 /. data; d3 = Sqrt[ (L3 Cos[f3]+u)^2 + (L3 Sin[f3]+v)^2 ] - L3 /. data; :[font = subsubsection; inactive; preserveAspect; startGroup] Elastic Potential Energy :[font = text; inactive; preserveAspect] Remember that the elastic energy stored in a single bar or spring is 1/2 k d^2. :[font = input; preserveAspect; startGroup] U[u_,v_] = 1/2 k1 d1^2 + 1/2 k2 d2^2 + 1/2 k3 d3^2 /. data :[font = output; output; inactive; preserveAspect; endGroup; endGroup] 75000.*(-100. + ((86.6025403784439 + u)^2 + (-50. + v)^2)^(1/2))^2 + 100000.*(-75. + ((-43.01823272632847 + u)^2 + (61.43640332167438 + v)^2)^(1/2))^2 + 100000.*(-75. + ((43.01823272632847 + u)^2 + (61.43640332167438 + v)^2)^(1/2))^2 ;[o] 2 2 75000. (-100. + Sqrt[(86.6025 + u) + (-50. + v) ]) 2 + 100000. (-75. + 2 2 2 Sqrt[(-43.0182 + u) + (61.4364 + v) ]) + 2 100000. (-75. + Sqrt[(43.0182 + u) + 2 2 (61.4364 + v) ]) :[font = subsubsection; inactive; preserveAspect; startGroup] Potential Energy of the Load :[font = input; preserveAspect; startGroup] P[u_,v_] = F Cos[fF] u + F Sin[fF] v /. data :[font = output; output; inactive; preserveAspect; endGroup; endGroup] 1299.038105676658*u + 750.*v ;[o] 1299.04 u + 750. v :[font = subsubsection; inactive; preserveAspect; startGroup] Total Potential Energy of the Structure :[font = input; preserveAspect] T[u_,v_] = U[u,v] - P[u,v]; :[font = text; inactive; preserveAspect] Here's a picture of total potential energy -- looks like there is a minimum in there somewhere. So we go after it with the Findminimum function. :[font = input; preserveAspect; startGroup] Plot3D[ T[u,v], {u,-.03,.03},{v,-.03,.03}] :[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; pictureLeft = 34; pictureWidth = 282; pictureHeight = 180] %! %%Creator: Mathematica %%AspectRatio: .63905 MathPictureStart %% SurfaceGraphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.025121 1.004836 -0.145751 1.004836 [ [(-0.02)] .31274 .60094 .02386 -1 Msboxa [(0)] .20856 .54491 .03565 -1 Msboxa [(0.02)] .09002 .48116 .04926 -1 Msboxa [(-0.02)] .14996 .11922 -0.04431 1 Msboxa [(0)] .37607 .07852 -0.01786 1 Msboxa [(0.02)] .61651 .03524 .01055 1 Msboxa [(0)] .0282 .16388 1 -0.17829 Msboxa [(100)] .02361 .24413 1 -0.16734 Msboxa [(200)] .01893 .3259 1 -0.15617 Msboxa [(300)] .01416 .40924 1 -0.14476 Msboxa [ 0 0 0 0 ] [ 1 .63905 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g p p .002 w .36047 .61393 m .02512 .43333 L s P p .002 w .31304 .58839 m .31319 .58211 L s P [(-0.02)] .31274 .60094 .02386 -1 Mshowa p .002 w .20901 .53236 m .20923 .52608 L s P [(0)] .20856 .54491 .03565 -1 Mshowa p .002 w .09064 .46861 m .09095 .46234 L s P [(0.02)] .09002 .48116 .04926 -1 Mshowa p .001 w .29325 .57773 m .29335 .57396 L s P p .001 w .27298 .56681 m .27308 .56304 L s P p .001 w .25219 .55562 m .25231 .55185 L s P p .001 w .23087 .54414 m .231 .54037 L s P p .001 w .18657 .52028 m .18671 .51651 L s P p .001 w .16354 .50787 m .16369 .50411 L s P p .001 w .13989 .49514 m .14006 .49137 L s P p .001 w .1156 .48205 m .11577 .47829 L s P p .001 w .33235 .59879 m .33244 .59502 L s P p .001 w .35121 .60894 m .35128 .60518 L s P p .001 w .06498 .45479 m .06518 .45103 L s P p .001 w .0386 .44058 m .0388 .43682 L s P P p p .002 w .04116 .15123 m .74284 .02512 L s P p .002 w .1494 .13177 m .14913 .13805 L s P [(-0.02)] .14996 .11922 -0.04431 1 Mshowa p .002 w .37585 .09108 m .37574 .09736 L s P [(0)] .37607 .07852 -0.01786 1 Mshowa p .002 w .61664 .0478 m .61671 .05408 L s P [(0.02)] .61651 .03524 .01055 1 Mshowa p .001 w .19361 .12383 m .19346 .12759 L s P p .001 w .23834 .11579 m .23822 .11955 L s P p .001 w .28362 .10765 m .28352 .11142 L s P p .001 w .32946 .09941 m .32937 .10318 L s P p .001 w .42282 .08263 m .42277 .0864 L s P p .001 w .47037 .07409 m .47034 .07786 L s P p .001 w .51852 .06544 m .51851 .0692 L s P p .001 w .56727 .05667 m .56729 .06044 L s P p .001 w .10572 .13962 m .10554 .14339 L s P p .001 w .06256 .14738 m .06235 .15114 L s P p .001 w .66664 .03882 m .6667 .04258 L s P p .001 w .71728 .02972 m .71736 .03348 L s P P p p .002 w .04116 .15123 m .02512 .43333 L s P p .002 w .04057 .16168 m .04675 .16058 L s P [(0)] .0282 .16388 1 -0.17829 Mshowa p .002 w .036 .24206 m .04219 .24102 L s P [(100)] .02361 .24413 1 -0.16734 Mshowa p .002 w .03134 .32397 m .03754 .323 L s P [(200)] .01893 .3259 1 -0.15617 Mshowa p .002 w .02659 .40744 m .03281 .40654 L s P [(300)] .01416 .40924 1 -0.14476 Mshowa p .001 w .03966 .17764 m .04337 .17698 L s P p .001 w .03875 .19365 m .04246 .19301 L s P p .001 w .03784 .20973 m .04155 .20909 L s P p .001 w .03692 .22586 m .04063 .22523 L s P p .001 w .03507 .25832 m .03879 .2577 L s P p .001 w .03415 .27464 m .03786 .27403 L s P p .001 w .03321 .29102 m .03693 .29042 L s P p .001 w .03228 .30746 m .036 .30687 L s P p .001 w .0304 .34053 m .03412 .33996 L s P p .001 w .02945 .35716 m .03318 .3566 L s P p .001 w .0285 .37386 m .03223 .3733 L s P p .001 w .02755 .39062 m .03128 .39007 L s P p .001 w .02563 .42432 m .02936 .42379 L s P P 0 0 m 1 0 L 1 .63905 L 0 .63905 L closepath clip newpath p .002 w .36489 .37548 m .36047 .61393 L s .36047 .61393 m .97488 .54562 L s .97488 .54562 m .96212 .29036 L s .96212 .29036 m .36489 .37548 L s .04116 .15123 m .74284 .02512 L s .74284 .02512 m .75066 .33086 L s .75066 .33086 m .02512 .43333 L s .02512 .43333 m .04116 .15123 L s .36489 .37548 m .36047 .61393 L s .36047 .61393 m .02512 .43333 L s .02512 .43333 m .04116 .15123 L s .04116 .15123 m .36489 .37548 L s .96212 .29036 m .74284 .02512 L s .74284 .02512 m .75066 .33086 L s .75066 .33086 m .97488 .54562 L s .97488 .54562 m .96212 .29036 L s P p .744 .706 .816 r .0015 w .36152 .55719 .4024 .53025 .38334 .49891 .34207 .52706 Metetra .752 .722 .824 r .34207 .52706 .38334 .49891 .36381 .4701 .32213 .4995 Metetra .761 .739 .833 r .32213 .4995 .36381 .4701 .34379 .44388 .30166 .47454 Metetra .771 .758 .841 r .30166 .47454 .34379 .44388 .32322 .4203 .28062 .45227 Metetra .78 .778 .851 r .28062 .45227 .32322 .4203 .30207 .39945 .25898 .43274 Metetra .791 .8 .86 r .25898 .43274 .30207 .39945 .2803 .38139 .23667 .41604 Metetra .801 .824 .869 r .23667 .41604 .2803 .38139 .25784 .36621 .21365 .40228 Metetra .812 .849 .877 r .21365 .40228 .25784 .36621 .23466 .35403 .18986 .39154 Metetra .821 .875 .885 r .18986 .39154 .23466 .35403 .21068 .34495 .16524 .38395 Metetra .83 .903 .89 r .16524 .38395 .21068 .34495 .18584 .3391 .13972 .37965 Metetra .836 .93 .892 r .13972 .37965 .18584 .3391 .16008 .33663 .11323 .37879 Metetra .838 .955 .89 r .11323 .37879 .16008 .33663 .13332 .33769 .08569 .38152 Metetra .835 .977 .88 r .08569 .38152 .13332 .33769 .10547 .34248 .05701 .38805 Metetra .825 .993 .862 r .05701 .38805 .10547 .34248 .07643 .35119 .0271 .39857 Metetra .73 .698 .82 r .4024 .53025 .44347 .50711 .42479 .47457 .38334 .49891 Metetra .738 .714 .829 r .38334 .49891 .42479 .47457 .40566 .44455 .36381 .4701 Metetra .746 .731 .838 r .36381 .4701 .40566 .44455 .38607 .41709 .34379 .44388 Metetra .755 .75 .848 r .34379 .44388 .38607 .41709 .36596 .39225 .32322 .4203 Metetra .764 .771 .858 r .32322 .4203 .36596 .39225 .3453 .3701 .30207 .39945 Metetra .774 .794 .869 r .30207 .39945 .3453 .3701 .32405 .35072 .2803 .38139 Metetra .784 .818 .879 r .2803 .38139 .32405 .35072 .30214 .33419 .25784 .36621 Metetra .794 .844 .889 r .25784 .36621 .30214 .33419 .27955 .32061 .23466 .35403 Metetra .803 .872 .898 r .23466 .35403 .27955 .32061 .25619 .31009 .21068 .34495 Metetra .811 .901 .905 r .21068 .34495 .25619 .31009 .23202 .30275 .18584 .3391 Metetra .815 .929 .909 r .18584 .3391 .23202 .30275 .20697 .29874 .16008 .33663 Metetra .816 .956 .906 r .16008 .33663 .20697 .29874 .18096 .29821 .13332 .33769 Metetra .81 .978 .896 r .13332 .33769 .18096 .29821 .15391 .30134 .10547 .34248 Metetra .795 .993 .876 r .10547 .34248 .15391 .30134 .12573 .30833 .07643 .35119 Metetra .715 .689 .824 r .44347 .50711 .4848 .48777 .46648 .45406 .42479 .47457 Metetra .722 .705 .833 r .42479 .47457 .46648 .45406 .44775 .42285 .40566 .44455 Metetra .73 .722 .844 r .40566 .44455 .44775 .42285 .42857 .39418 .38607 .41709 Metetra .738 .742 .854 r .38607 .41709 .42857 .39418 .40891 .36811 .36596 .39225 Metetra .747 .763 .866 r .36596 .39225 .40891 .36811 .38873 .3447 .3453 .3701 Metetra .756 .786 .878 r .3453 .3701 .38873 .3447 .36798 .32404 .32405 .35072 Metetra .765 .811 .89 r .32405 .35072 .36798 .32404 .34661 .30619 .30214 .33419 Metetra .774 .838 .901 r .30214 .33419 .34661 .30619 .32459 .29126 .27955 .32061 Metetra .782 .867 .912 r .27955 .32061 .32459 .29126 .30185 .27935 .25619 .31009 Metetra .788 .897 .92 r .25619 .31009 .30185 .27935 .27833 .27059 .23202 .30275 Metetra .791 .927 .925 r .23202 .30275 .27833 .27059 .25396 .26511 .20697 .29874 Metetra .789 .955 .923 r .20697 .29874 .25396 .26511 .22869 .26305 .18096 .29821 Metetra .779 .977 .913 r .18096 .29821 .22869 .26305 .20242 .2646 .15391 .30134 Metetra .759 .99 .889 r .15391 .30134 .20242 .2646 .17508 .26995 .12573 .30833 Metetra .699 .679 .827 r .4848 .48777 .52644 .47226 .50848 .43739 .46648 .45406 Metetra .706 .695 .837 r .46648 .45406 .50848 .43739 .49013 .40501 .44775 .42285 Metetra .712 .712 .848 r .44775 .42285 .49013 .40501 .47136 .37516 .42857 .39418 Metetra .72 .731 .86 r .42857 .39418 .47136 .37516 .45213 .34788 .40891 .36811 Metetra .727 .753 .873 r .40891 .36811 .45213 .34788 .43241 .32326 .38873 .3447 Metetra .735 .776 .886 r .38873 .3447 .43241 .32326 .41216 .30134 .36798 .32404 Metetra .743 .802 .899 r .36798 .32404 .41216 .30134 .39132 .28222 .34661 .30619 Metetra .751 .83 .913 r .34661 .30619 .39132 .28222 .36985 .26599 .32459 .29126 Metetra .757 .86 .925 r .32459 .29126 .36985 .26599 .34771 .25274 .30185 .27935 Metetra .762 .891 .935 r .30185 .27935 .34771 .25274 .32482 .24261 .27833 .27059 Metetra .762 .922 .941 r .27833 .27059 .32482 .24261 .30114 .23571 .25396 .26511 Metetra .757 .95 .94 r .25396 .26511 .30114 .23571 .27658 .2322 .22869 .26305 Metetra .742 .972 .928 r .22869 .26305 .27658 .2322 .25108 .23224 .20242 .2646 Metetra .715 .982 .901 r .20242 .2646 .25108 .23224 .22456 .23602 .17508 .26995 Metetra .682 .668 .83 r .52644 .47226 .56845 .46059 .55083 .42459 .50848 .43739 Metetra .688 .684 .841 r .50848 .43739 .55083 .42459 .53286 .39106 .49013 .40501 Metetra .693 .701 .853 r .49013 .40501 .53286 .39106 .51449 .36004 .47136 .37516 Metetra .699 .72 .865 r .47136 .37516 .51449 .36004 .49569 .3316 .45213 .34788 Metetra .706 .741 .879 r .45213 .34788 .49569 .3316 .47642 .30577 .43241 .32326 Metetra .713 .765 .893 r .43241 .32326 .47642 .30577 .45665 .28265 .41216 .30134 Metetra .719 .791 .908 r .41216 .30134 .45665 .28265 .43633 .26229 .39132 .28222 Metetra .725 .819 .923 r .39132 .28222 .43633 .26229 .41541 .2448 .36985 .26599 Metetra .73 .85 .938 r .36985 .26599 .41541 .2448 .39385 .23026 .34771 .25274 Metetra .731 .882 .95 r .34771 .25274 .39385 .23026 .37159 .21881 .32482 .24261 Metetra .729 .913 .957 r .32482 .24261 .37159 .21881 .34857 .21055 .30114 .23571 Metetra .719 .941 .957 r .30114 .23571 .34857 .21055 .32472 .20564 .27658 .2322 Metetra .698 .962 .943 r .27658 .2322 .32472 .20564 .29997 .20425 .25108 .23224 Metetra .663 .969 .912 r .25108 .23224 .29997 .20425 .27425 .20654 .22456 .23602 Metetra .664 .657 .833 r .56845 .46059 .61089 .45282 .59362 .41569 .55083 .42459 Metetra .668 .672 .844 r .55083 .42459 .59362 .41569 .57601 .38103 .53286 .39106 Metetra .673 .688 .856 r .53286 .39106 .57601 .38103 .55803 .34887 .51449 .36004 Metetra .678 .707 .87 r .51449 .36004 .55803 .34887 .53964 .31927 .49569 .3316 Metetra .683 .728 .884 r .49569 .3316 .53964 .31927 .52082 .29229 .47642 .30577 Metetra .688 .751 .9 r .47642 .30577 .52082 .29229 .50153 .26798 .45665 .28265 Metetra .692 .777 .916 r .45665 .28265 .50153 .26798 .48171 .24642 .43633 .26229 Metetra .696 .806 .933 r .43633 .26229 .48171 .24642 .46133 .22771 .41541 .2448 Metetra .698 .837 .949 r .41541 .2448 .46133 .22771 .44035 .21193 .39385 .23026 Metetra .696 .869 .963 r .39385 .23026 .44035 .21193 .4187 .1992 .37159 .21881 Metetra .69 .9 .972 r .37159 .21881 .4187 .1992 .39633 .18965 .34857 .21055 Metetra .674 .928 .971 r .34857 .21055 .39633 .18965 .37317 .18341 .32472 .20564 Metetra .647 .946 .956 r .32472 .20564 .37317 .18341 .34917 .18064 .29997 .20425 Metetra .603 .948 .919 r .29997 .20425 .34917 .18064 .32423 .18152 .27425 .20654 Metetra .645 .644 .834 r .61089 .45282 .65384 .44898 .6369 .41075 .59362 .41569 Metetra .648 .658 .846 r .59362 .41569 .6369 .41075 .61964 .37497 .57601 .38103 Metetra .651 .674 .859 r .57601 .38103 .61964 .37497 .60204 .34169 .55803 .34887 Metetra .654 .693 .873 r .55803 .34887 .60204 .34169 .58407 .31096 .53964 .31927 Metetra .658 .713 .889 r .53964 .31927 .58407 .31096 .56569 .28284 .52082 .29229 Metetra .66 .736 .906 r .52082 .29229 .56569 .28284 .54686 .25738 .50153 .26798 Metetra .663 .761 .923 r .50153 .26798 .54686 .25738 .52754 .23466 .48171 .24642 Metetra .664 .789 .942 r .48171 .24642 .52754 .23466 .50769 .21476 .46133 .22771 Metetra .662 .82 .959 r .46133 .22771 .50769 .21476 .48727 .19778 .44035 .21193 Metetra .657 .851 .975 r .44035 .21193 .48727 .19778 .46623 .18383 .4187 .1992 Metetra .645 .882 .984 r .4187 .1992 .46623 .18383 .4445 .17302 .39633 .18965 Metetra .623 .908 .983 r .39633 .18965 .4445 .17302 .42203 .16551 .37317 .18341 Metetra .587 .922 .965 r .37317 .18341 .42203 .16551 .39876 .16143 .34917 .18064 Metetra .532 .918 .922 r .34917 .18064 .39876 .16143 .3746 .16097 .32423 .18152 Metetra .625 .63 .835 r .65384 .44898 .69735 .44915 .68074 .40981 .6369 .41075 Metetra .627 .644 .848 r .6369 .41075 .68074 .40981 .66383 .37293 .61964 .37497 Metetra .628 .659 .861 r .61964 .37497 .66383 .37293 .64661 .33855 .60204 .34169 Metetra .63 .677 .876 r .60204 .34169 .64661 .33855 .62904 .30671 .58407 .31096 Metetra .631 .696 .892 r .58407 .31096 .62904 .30671 .61108 .27747 .56569 .28284 Metetra .631 .718 .91 r .56569 .28284 .61108 .27747 .59271 .25089 .54686 .25738 Metetra .63 .743 .929 r .54686 .25738 .59271 .25089 .57389 .22704 .52754 .23466 Metetra .628 .77 .948 r .52754 .23466 .57389 .22704 .55457 .206 .50769 .21476 Metetra .623 .799 .967 r .50769 .21476 .55457 .206 .53471 .18786 .48727 .19778 Metetra .612 .829 .983 r .48727 .19778 .53471 .18786 .51426 .17273 .46623 .18383 Metetra .594 .858 .994 r .46623 .18383 .51426 .17273 .49317 .16073 .4445 .17302 Metetra .564 .881 .992 r .4445 .17302 .49317 .16073 .47138 .15199 .42203 .16551 Metetra .518 .891 .97 r .42203 .16551 .47138 .15199 .44883 .14667 .39876 .16143 Metetra .453 .878 .919 r .39876 .16143 .44883 .14667 .42544 .14494 .3746 .16097 Metetra .605 .616 .836 r .69735 .44915 .7415 .4534 .72521 .41296 .68074 .40981 Metetra .604 .629 .848 r .68074 .40981 .72521 .41296 .70865 .375 .66383 .37293 Metetra .604 .643 .862 r .66383 .37293 .70865 .375 .69179 .33953 .64661 .33855 Metetra .603 .659 .877 r .64661 .33855 .69179 .33953 .67462 .3066 .62904 .30671 Metetra .602 .677 .894 r .62904 .30671 .67462 .3066 .65709 .27627 .61108 .27747 Metetra .6 .698 .912 r .61108 .27747 .65709 .27627 .63918 .24859 .59271 .25089 Metetra .596 .721 .932 r .59271 .25089 .63918 .24859 .62084 .22363 .57389 .22704 Metetra .589 .747 .952 r .57389 .22704 .62084 .22363 .60204 .20148 .55457 .206 Metetra .579 .774 .972 r .55457 .206 .60204 .20148 .58273 .18222 .53471 .18786 Metetra .563 .802 .989 r .53471 .18786 .58273 .18222 .56288 .16596 .51426 .17273 Metetra .537 .828 .999 r .51426 .17273 .56288 .16596 .54242 .15281 .49317 .16073 Metetra .499 .847 .995 r .49317 .16073 .54242 .15281 .5213 .14291 .47138 .15199 Metetra .443 .85 .968 r .47138 .15199 .5213 .14291 .49947 .13641 .44883 .14667 Metetra .366 .829 .909 r .44883 .14667 .49947 .13641 .47685 .13347 .42544 .14494 Metetra .583 .601 .835 r .7415 .4534 .78636 .46181 .77038 .42029 .72521 .41296 Metetra .581 .612 .848 r .72521 .41296 .77038 .42029 .75416 .38124 .70865 .375 Metetra .579 .625 .862 r .70865 .375 .75416 .38124 .73768 .3447 .69179 .33953 Metetra .576 .64 .877 r .69179 .33953 .73768 .3447 .7209 .3107 .67462 .3066 Metetra .572 .657 .894 r .67462 .3066 .7209 .3107 .70379 .2793 .65709 .27627 Metetra .566 .676 .913 r .65709 .27627 .70379 .2793 .68633 .25055 .63918 .24859 Metetra .559 .697 .933 r .63918 .24859 .68633 .25055 .66847 .22452 .62084 .22363 Metetra .548 .721 .953 r .62084 .22363 .66847 .22452 .65019 .20129 .60204 .20148 Metetra .532 .745 .973 r .60204 .20148 .65019 .20129 .63144 .18095 .58273 .18222 Metetra .509 .77 .99 r .58273 .18222 .63144 .18095 .61217 .1636 .56288 .16596 Metetra .476 .792 .999 r .56288 .16596 .61217 .1636 .59234 .14935 .54242 .15281 Metetra .427 .804 .992 r .54242 .15281 .59234 .14935 .57189 .13834 .5213 .14291 Metetra .36 .8 .96 r .5213 .14291 .57189 .13834 .55078 .13071 .49947 .13641 Metetra .274 .77 .892 r .49947 .13641 .55078 .13071 .52892 .12664 .47685 .13347 Metetra .561 .585 .834 r .78636 .46181 .83201 .47448 .81635 .43189 .77038 .42029 Metetra .558 .595 .847 r .77038 .42029 .81635 .43189 .80046 .39177 .75416 .38124 Metetra .553 .607 .861 r .75416 .38124 .80046 .39177 .78434 .35416 .73768 .3447 Metetra .548 .62 .876 r .73768 .3447 .78434 .35416 .76795 .31911 .7209 .3107 Metetra .541 .635 .893 r .7209 .3107 .76795 .31911 .75126 .28666 .70379 .2793 Metetra .532 .652 .912 r .70379 .2793 .75126 .28666 .73425 .25686 .68633 .25055 Metetra .52 .671 .932 r .68633 .25055 .73425 .25686 .71688 .22979 .66847 .22452 Metetra .504 .691 .952 r .66847 .22452 .71688 .22979 .69911 .20551 .65019 .20129 Metetra .482 .712 .972 r .65019 .20129 .69911 .20551 .68091 .18413 .63144 .18095 Metetra .452 .733 .987 r .63144 .18095 .68091 .18413 .66223 .16573 .61217 .1636 Metetra .41 .749 .994 r .61217 .1636 .66223 .16573 .64303 .15043 .59234 .14935 Metetra .351 .755 .983 r .59234 .14935 .64303 .15043 .62325 .13837 .57189 .13834 Metetra .274 .742 .944 r .57189 .13834 .62325 .13837 .60285 .12968 .55078 .13071 Metetra .178 .703 .868 r .55078 .13071 .60285 .12968 .58176 .12453 .52892 .12664 Metetra .539 .568 .832 r .83201 .47448 .87854 .49154 .86318 .44787 .81635 .43189 Metetra .533 .577 .845 r .81635 .43189 .86318 .44787 .84763 .40669 .80046 .39177 Metetra .527 .587 .858 r .80046 .39177 .84763 .40669 .83187 .36804 .78434 .35416 Metetra .518 .599 .874 r .78434 .35416 .83187 .36804 .81587 .33194 .76795 .31911 Metetra .508 .612 .89 r .76795 .31911 .81587 .33194 .7996 .29846 .75126 .28666 Metetra .496 .626 .909 r .75126 .28666 .7996 .29846 .78303 .26764 .73425 .25686 Metetra .48 .642 .928 r .73425 .25686 .78303 .26764 .76614 .23955 .71688 .22979 Metetra .459 .659 .948 r .71688 .22979 .76614 .23955 .74889 .21426 .69911 .20551 Metetra .43 .676 .966 r .69911 .20551 .74889 .21426 .73124 .19187 .68091 .18413 Metetra .393 .691 .98 r .68091 .18413 .73124 .19187 .71315 .17247 .66223 .16573 Metetra .341 .701 .983 r .66223 .16573 .71315 .17247 .69458 .15616 .64303 .15043 Metetra .273 .699 .967 r .64303 .15043 .69458 .15616 .67548 .14309 .62325 .13837 Metetra .186 .677 .922 r .62325 .13837 .67548 .14309 .65579 .1334 .60285 .12968 Metetra .084 .63 .838 r .60285 .12968 .65579 .1334 .63547 .12724 .58176 .12453 Metetra .517 .551 .83 r .87854 .49154 .92603 .51312 .91097 .46838 .86318 .44787 Metetra .509 .558 .842 r .86318 .44787 .91097 .46838 .89575 .42614 .84763 .40669 Metetra .5 .567 .855 r .84763 .40669 .89575 .42614 .88035 .38645 .83187 .36804 Metetra .489 .577 .87 r .83187 .36804 .88035 .38645 .86474 .34932 .81587 .33194 Metetra .476 .587 .886 r .81587 .33194 .86474 .34932 .84889 .31483 .7996 .29846 Metetra .459 .599 .903 r .7996 .29846 .84889 .31483 .83278 .28301 .78303 .26764 Metetra .439 .611 .922 r .78303 .26764 .83278 .28301 .81637 .25393 .76614 .23955 Metetra .412 .624 .94 r .76614 .23955 .81637 .25393 .79963 .22766 .74889 .21426 Metetra .378 .637 .956 r .74889 .21426 .79963 .22766 .78254 .2043 .73124 .19187 Metetra .332 .646 .967 r .73124 .19187 .78254 .2043 .76504 .18393 .71315 .17247 Metetra .272 .649 .967 r .71315 .17247 .76504 .18393 .7471 .16667 .69458 .15616 Metetra .195 .638 .946 r .69458 .15616 .7471 .16667 .72868 .15265 .67548 .14309 Metetra .1 .609 .894 r .67548 .14309 .72868 .15265 .70972 .14201 .65579 .1334 Metetra 0 .554 .804 r .65579 .1334 .70972 .14201 .69017 .13491 .63547 .12724 Metetra .494 .534 .826 r .92603 .51312 .97457 .53937 .95982 .49355 .91097 .46838 Metetra .484 .54 .838 r .91097 .46838 .95982 .49355 .94493 .45027 .89575 .42614 Metetra .473 .546 .851 r .89575 .42614 .94493 .45027 .92989 .40954 .88035 .38645 Metetra .459 .554 .865 r .88035 .38645 .92989 .40954 .91467 .37141 .86474 .34932 Metetra .443 .562 .88 r .86474 .34932 .91467 .37141 .89924 .33591 .84889 .31483 Metetra .423 .571 .896 r .84889 .31483 .89924 .33591 .88358 .30311 .83278 .28301 Metetra .397 .58 .913 r .83278 .28301 .88358 .30311 .86766 .27307 .81637 .25393 Metetra .365 .588 .93 r .81637 .25393 .86766 .27307 .85144 .24585 .79963 .22766 Metetra .325 .595 .943 r .79963 .22766 .85144 .24585 .8349 .22155 .78254 .2043 Metetra .272 .598 .951 r .78254 .2043 .8349 .22155 .81801 .20026 .76504 .18393 Metetra .204 .594 .946 r .76504 .18393 .81801 .20026 .80071 .18209 .7471 .16667 Metetra .119 .576 .919 r .7471 .16667 .80071 .18209 .78297 .16718 .72868 .15265 Metetra .018 .538 .861 r .72868 .15265 .78297 .16718 .76474 .15565 .70972 .14201 Metetra 0 .479 .767 r .70972 .14201 .76474 .15565 .74597 .14767 .69017 .13491 Metetra P p .002 w .04116 .15123 m .74284 .02512 L s .74284 .02512 m .75066 .33086 L s .75066 .33086 m .02512 .43333 L s .02512 .43333 m .04116 .15123 L s .96212 .29036 m .74284 .02512 L s .74284 .02512 m .75066 .33086 L s .75066 .33086 m .97488 .54562 L s .97488 .54562 m .96212 .29036 L s P p p .002 w .04116 .15123 m .02512 .43333 L s P p .002 w .04057 .16168 m .04675 .16058 L s P [(0)] .0282 .16388 1 -0.17829 Mshowa p .002 w .036 .24206 m .04219 .24102 L s P [(100)] .02361 .24413 1 -0.16734 Mshowa p .002 w .03134 .32397 m .03754 .323 L s P [(200)] .01893 .3259 1 -0.15617 Mshowa p .002 w .02659 .40744 m .03281 .40654 L s P [(300)] .01416 .40924 1 -0.14476 Mshowa p .001 w .03966 .17764 m .04337 .17698 L s P p .001 w .03875 .19365 m .04246 .19301 L s P p .001 w .03784 .20973 m .04155 .20909 L s P p .001 w .03692 .22586 m .04063 .22523 L s P p .001 w .03507 .25832 m .03879 .2577 L s P p .001 w .03415 .27464 m .03786 .27403 L s P p .001 w .03321 .29102 m .03693 .29042 L s P p .001 w .03228 .30746 m .036 .30687 L s P p .001 w .0304 .34053 m .03412 .33996 L s P p .001 w .02945 .35716 m .03318 .3566 L s P p .001 w .0285 .37386 m .03223 .3733 L s P p .001 w .02755 .39062 m .03128 .39007 L s P p .001 w .02563 .42432 m .02936 .42379 L s P P % End of Graphics MathPictureEnd :[font = output; output; inactive; preserveAspect; endGroup; endGroup; endGroup] SurfaceGraphics["<<>>"] ;[o] -SurfaceGraphics- :[font = subsection; inactive; preserveAspect; startGroup] Easiest Way to Get the Answer --Nonlinear prob. :[font = text; inactive; preserveAspect] We seek the values of u and v which will minimize this function of two variables T(u, v). We use the power of Mathematica and apply the FindMinimum command with a reasonable starting estimate for u = 0 and v = 0. ;[s] 3:0,0;111,1;122,2;213,-1; 3:1,13,10,Times,0,14,0,0,0;1,13,10,Times,3,14,0,0,0;1,13,10,Times,0,14,0,0,0; :[font = input; preserveAspect; startGroup] sol1=FindMinimum[ T[u,v], {u,0}, {v,0}] :[font = output; output; inactive; preserveAspect; endGroup] {-5.536156242121855, {u -> 0.006331729542898658, v -> 0.003795998527056068}} ;[o] {-5.53616, {u -> 0.00633173, v -> 0.003796}} :[font = text; inactive; preserveAspect] And now let us explain just what we have actually found here and interpret it in our problem, e.g., with our determination of u and v we have found "exactly" how far the load has moved. ;[s] 1:0,0;185,-1; 1:1,13,10,Times,0,14,0,0,0; :[font = input; preserveAspect; startGroup] Sqrt[ u^2 + v^2] /. sol1[[2]] :[font = output; output; inactive; preserveAspect; endGroup; endGroup] 0.007382438880331316 ;[o] 0.00738244 :[font = subsection; inactive; preserveAspect; startGroup] A More Explicit Way to Get the Answer -- Nonlinear Problem :[font = subsubsection; inactive; preserveAspect; startGroup] Derivatives of the total potential energy. :[font = input; preserveAspect; endGroup] e1 = D[ T[u,v], u ] == 0; e2 = D[ T[u,v], v] == 0; :[font = subsubsection; inactive; preserveAspect; startGroup] Solution of the resulting non-linear system :[font = input; preserveAspect; startGroup] FindRoot[ {e1,e2}, {u,0}, {v,0} ] :[font = output; output; inactive; preserveAspect; endGroup; endGroup; endGroup] {u -> 0.006331729542231459, v -> 0.003795998528297142} ;[o] {u -> 0.00633173, v -> 0.003796} :[font = subsection; inactive; Cclosed; preserveAspect; startGroup] Linear Solution :[font = subsubsection; inactive; preserveAspect; startGroup] -- linearize the expressions for the displacements by expanding in a first degree Taylor series truncating higher order terms. ;[s] 1:0,0;128,-1; 1:1,12,9,Times,1,14,0,0,0; :[font = input; preserveAspect; startGroup] d1l =Series[ d1, {u,0,1}, {v,0,1}] //Normal //Expand :[font = output; output; inactive; preserveAspect; endGroup] 0.866025403784439*u - 0.5*v + 0.004330127018922194*u*v ;[o] 0.866025 u - 0.5 v + 0.00433013 u v :[font = input; preserveAspect; startGroup] d1l = d1l - d1l[[3]] //Chop :[font = output; output; inactive; preserveAspect; endGroup] 0.866025403784439*u - 0.5*v ;[o] 0.866025 u - 0.5 v :[font = input; preserveAspect; endGroup] d2l =Series[ d2, {u,0,1}, {v,0,1}] //Normal //Expand; d2l = d2l - d2l[[3]] //Chop; d3l = Series[ d3, {u,0,1}, {v,0,1}] //Normal //Expand; d3l = d3l - d3l[[3]] //Chop; :[font = subsubsection; inactive; preserveAspect; startGroup] Write an elastic potential energy function -- a quadratic :[font = input; preserveAspect; startGroup] Ul[u_,v_] = 1/2 k1 d1l^2 + 1/2 k2 d2l^2 + 1/2 k3 d3l^2 /. data :[font = output; output; inactive; preserveAspect; endGroup; endGroup] 75000.*(0.866025403784439*u - 0.5*v)^2 + 100000.*(-0.5735764363510463*u + 0.819152044288992*v)^2 + 100000.*(0.5735764363510463*u + 0.819152044288992*v)^2 ;[o] 2 75000. (0.866025 u - 0.5 v) + 2 100000. (-0.573576 u + 0.819152 v) + 2 100000. (0.573576 u + 0.819152 v) :[font = subsubsection; inactive; preserveAspect; startGroup] Linearized Total Potential Energy -- also a quadratic function :[font = input; preserveAspect; endGroup] Tl[u_,v_] = Ul[u,v] - P[u,v]; :[font = subsubsection; inactive; preserveAspect; startGroup] Equilibrium equations are linear! :[font = input; preserveAspect; startGroup] e1l = Expand[D[Tl[u,v],u]] == 0 :[font = output; output; inactive; preserveAspect; endGroup] -1299.038105676658 + 244095.9713348664*u - 64951.9052838329*v == 0 ;[o] -1299.04 + 244096. u - 64951.9 v == 0 :[font = input; preserveAspect; startGroup] e2l = Expand[D[Tl[u,v],v]] == 0 :[font = output; output; inactive; preserveAspect; endGroup; endGroup] -750. - 64951.9052838329*u + 305904.0286651337*v == 0 ;[o] -750. - 64951.9 u + 305904. v == 0 :[font = subsubsection; inactive; preserveAspect; startGroup] Solution of linear equations :[font = input; preserveAspect; startGroup] Solve[ {e1l,e2l}, {u,v}] :[font = output; output; inactive; preserveAspect; endGroup; endGroup] {{u -> 0.006331971290609251, v -> 0.003796202372995948}} ;[o] {{u -> 0.00633197, v -> 0.0037962}} :[font = subsubsection; inactive; preserveAspect; endGroup; endGroup] Comparison with nonlinear solution -- good to around the 4th significant figure. :[font = section; inactive; Cclosed; preserveAspect; startGroup] ISSUES IN SOLUTION :[font = text; inactive; preserveAspect; endGroup; endGroup] An important issue involves the ease with which the student is allowed to find the minimum. For some CAS experts, the use of FindMinimum is obvious. But do they know what is happening? ^*)